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Popular >

integral of e^{-it}

Solution

\int e^{- i t} d t

Solution

sin (t) + i cos (t) + C

Solution steps

\int e^{- i t} d t

Simplify

e^{- i t} : cos (t) - i sin (t)

= \int cos (t) - i sin (t) d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (t) d t - \int i sin (t) d t

\int cos (t) d t = sin (t)

\int i sin (t) d t = - i cos (t)

= sin (t) - (- i cos (t))

Simplify

= sin (t) + i cos (t)

Add a constant to the solution

= sin (t) + i cos (t) + C

Popular Examples

integral of (9x^2-3sqrt(x))/x

\int \frac{9 x ^{2} - 3 x}{x} d x

integral of sec^9(x)tan^5(x)

\int sec^{9} (x) tan^{5} (x) d x

integral of ((u+1))/(u(u+2))

\int \frac{( u + 1 )}{u ( u + 2 )} d u

integral of 4x^3+3x^2-4x

\int 4 x^{3} + 3 x^{2} - 4 x d x

integral of (9x)/(1+x^2)

\int \frac{9 x}{1 + x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of e^{-it} ?
The integral of e^{-it} is sin(t)+icos(t)+C